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Commit fe4127a6 authored by Alice Russell's avatar Alice Russell
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Re #16480 add documentation for the thermal neutron bk2bk functions

This includes docs for ThermalNeutronBk2BkExpAlpha, ThermalNeutronBk2BkExpBeta, ThermalNeutronBk2BkExpSigma and ThermalNeutronDtoTOFFunction
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.. _func-ThermalNeutronBk2BkExpAlpha:
===========================
ThermalNeutronBk2BkExpAlpha
===========================
.. index:: ThermalNeutronBk2BkExpAlpha
Description
-----------
ThermalNeutronBk2BkExpAlpha is a function to calculate :math:`\alpha` of :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`.
It is defined as
.. math:: \alpha(d_h) = \left(n\alpha_0 + \alpha_1 d_h + (1-n)\alpha_0^t - \frac{\alpha_1^t}{d_h}\right)^{-1}
where
.. math:: n = \frac{1}{2} \mathit{erfc}(\text{Width}(t_\text{cross} - d^{-1}))
and
.. math:: erfc(x) = 1-erf(x) = 1-\frac{2}{\sqrt{\pi}}\int_0^xe^{-u^2}du.
.. attributes::
.. properties::
.. categories::
.. sourcelink::
.. _func-ThermalNeutronBk2BkExpBeta:
==========================
ThermalNeutronBk2BkExpBeta
==========================
.. index:: ThermalNeutronBk2BkExpBeta
Description
-----------
ThermalNeutronBk2BkExpBeta is a function to calculate :math:`\beta` of :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`.
It is defined as
.. math:: \beta(d_h) = \left(n\beta_0 + \beta_1 d_h + (1-n)\beta_0^t - \frac{\beta_1^t}{d_h}\right)^{-1}
where
.. math:: n = \frac{1}{2} \mathit{erfc}(\text{Width}(t_\text{cross} - d^{-1}))
and
.. math:: erfc(x) = 1-erf(x) = 1-\frac{2}{\sqrt{\pi}}\int_0^xe^{-u^2}du.
.. attributes::
.. properties::
.. categories::
.. sourcelink::
.. _func-ThermalNeutronBk2BkExpSigma:
===========================
ThermalNeutronBk2BkExpSigma
===========================
.. index:: ThermalNeutronBk2BkExpSigma
Description
-----------
ThermalNeutronBk2BkExpSigma is a function to calculate :math:`\sigma` of :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`.
It is defined as
.. math:: \sigma(d_h) = \left(\sigma_0^2 + \sigma_1^2 + d_h^2 + \sigma_2^2 + d_h^4\right)^{0.5}
.. attributes::
.. properties::
.. categories::
.. sourcelink::
.. _func-ThermalNeutronDtoTOFFunction:
============================
ThermalNeutronDtoTOFFunction
============================
.. index:: ThermalNeutronDtoTOFFunction
Description
-----------
ThermalNeutronDtoTOFFunction is a function to calculate TOF from d-spacing values for :ref:`ThermalNeutronBk2BkExpConvPVoigt <func-ThermalNeutronBk2BkExpConvPVoigt>`.
It is defined as
.. math:: TOF = n(zero + dtt1 \cdot dh)+(1-n)(zero_t + dtt1t\cdot dh - \frac{dtt2t}{dh})
where
.. math:: n = \frac{1}{2} \mathit{erfc}(\text{Width}(t_\text{cross} - d^{-1})).
.. attributes::
.. properties::
.. categories::
.. sourcelink::
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